课程介绍

Linear algebra is a fundamental part of modern mathematics and has become a successful part of mathematical language. The applications of it have appeared in many fields and are spreading more rapidly than any other time in the past due to the advancement of the computer technology. Therefore, students are required to learn this course after they have finished Calculus.
In this course, knowledge of systems of linear equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors are introduced and studied. The main theme is the theory of systems of linear equations; the method of matrix and the idea of elementary operations for matrices are emphasized throughout this course. Students will learn basic concepts including: matrices, invertible matrices, block matrices, rank of a matrix, determinants, linear dependence and linear independence, subspace, bases, the dimension of a vector space, eigenvalues and eigenvectors and so on. The following sequence of problems will be researched: how to do basic operations of matrices, how to find the inverse and rank of a matrix using elementary row operations, how to determine whether a non-homogeneous system of linear equations has solutions or not and find them if it does, how to evaluate a determinant, how to determine whether a set of vectors is linear dependent or not, how to find NulA and ColA , and then find their dimensions and bases, how to find the eigenvalues and eigenvectors of a matrix, how to diagonalize a given matrix.

课程大纲

学习目标

Students are required to master essential concepts, theories, methods and skills of linear algebra in a one-semester course. They are also expected to use the basic knowledge of linear algebra to solve some practical problems

学习要求

1. Attend every class on time;
2. Participate in the discussion and carry out the given tasks;
3. Review topics introduced in class;
4. Complete homework for each class and submit it to the App before deadline;
5. Complete quizzes/mid-term exam;
6. Complete final exam.

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考核标准

Total points of this course include:
Attendance: 7%;
Homework projects: 7%;
Mid-term exam or quizzes: 7%;
Others: 9%;
Final Exam: 70%

教材教参

[1] David C. Lay, Linear Algebra and Its Applications (Third Edition), Publishing House of Electronics Industry, 2010.8.
[2] Gilbert Strang, Introduction to Linear Algebra (Third Edition), Wellesley-Cambridge Press, 2003.
[3] Steven J. Leon, Linear Algebra with Applications (Ninth Edition), China Machine Press, 2017.